$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 9x + 2$ and $ BC = 5x + 10$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {9x + 2} = {5x + 10}$ Solve for $x$ $ 4x = 8$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 9({2}) + 2$ $ BC = 5({2}) + 10$ $ AB = 18 + 2$ $ BC = 10 + 10$ $ AB = 20$ $ BC = 20$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {20} + {20}$ $ AC = 40$